Say we have an anarchist society where there is no private property and no one has authority over anyone else. There are only voluntary social organizational structures. If someone built a weapon, now they could coerce people into doing things for him and then start a government. Is there any way in anarchism that people could prevent this?

Anarchy is all about Voluntary, in which larger things are accomplished by voluntary associations with members who have freedom of entry and exit, thus Force is not part of the picture. Many may be in corporate form, with members purchasing stock with the clear intent of return. Where's the need for a "State"?

Oh, there will be capitalism and private property, as there is no "state" to prohibit such.
There will be self-defense plus private security companies. When the sovereign individual is judge, jury and executioner, criminals will naturally find a safer trade.